
Re: Number of lattice paths with given steps?
Posted:
Nov 20, 2012 11:01 PM


On Tue, 20 Nov 2012, IV wrote:
> I'm looking for a formula for calculating the number of lattice paths in a > rectangular quadratic integer lattice with given kind of steps and given > numbers of steps of each kind.
What's a rectangular quadratic integer lattice?
Is it, by some far fetched possibility, Z^2 with the product order, ie (j,k) <= (n,m) when j <= n, k <= m. Or do you simply mean Z^2 with no lattice order?
I suppose are there four kinds of steps, up, down, left, right and if some steps are missing, tough.
Now what the heck is a lattice path? Any finite path. Any finite path from a point? Any finite path from a point to another given point?
> That means all lattice paths with n1 steps (1,1), n2 steps (1,2), n3 > steps (1,3) and so on  the numbers n1, n2, n3, ... are given. > What constitutes the step (1,2)?
> Can somebody help? > I'm dubious as you wright stream of conscious nonsense comprehensible only by mind readers who refrain from reading your reprehensible mind.
> Was this problem already discussed in the literature?

